The SLLMWITQC (SEQ ID NO:126) peptide is derived from the NY-ESO-I protein that is expressed by a range of tumours (Chen et al., (1997) PNAS USA 94 1914-1918). The Class I HLA molecules of these cancerous cells present peptides from this protein, including SLLMWITQC (SEQ ID NO:126). Therefore, the SLLMWITQC (SEQ ID NO:126)-HLA-A2 complex provides a cancer marker that TCRs can target, for example for the purpose of delivering cytotoxic or immuno-stimulatory agents to the cancer cells. However, for that purpose it would be desirable if the TCR had a higher affinity and/or a slower off-rate for the peptide-HLA complex than native TCRs specific for that complex.